unitsize(1cm);

real r1 = 2;
real r2 = r1/2;
pair c1 = (r1/2, 0);
pair c2 = (-r1/2, 0);
path ellipse1 = ellipse(c1, r1, r2);
path ellipse2 = ellipse(c2, r1, r2);

picture intersection;
fill(intersection, ellipse1, mediumgray);
clip(intersection, ellipse2);

label("$A$", (c1.x, c1.y), E);
label("$B$", (c2.x, c2.y), W);
label("$A\cap B$", ((c1.x+c2.x)/2,(c1.y+c2.y)/2));

add(intersection);
draw(ellipse1);
draw(ellipse2);


